Given $ m \angle ABC = 5x + 133$, and $ m \angle CBD = 8x - 18$, find $m\angle ABC$. $B$ $A$ $D$ $C$
Explanation: From the diagram, we see that together ${\angle ABC}$ and ${\angle CBD}$ form ${\angle ABD}$ , so $ {m\angle ABC} + {m\angle CBD} = {m\angle ABD}$ Since $\angle ABD$ is a straight angle, we know ${m\angle ABD = 180}$ Substitute in the expressions that were given for each measure: $ {5x + 133} + {8x - 18} = {180}$ Combine like terms: $ 13x + 115 = 180$ Subtract $115$ from both sides: $ 13x = 65$ Divide both sides by $13$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $m\angle ABC$ $ m\angle ABC = 5({5}) + 133$ Simplify: $ {m\angle ABC = 25 + 133}$ So ${m\angle ABC = 158}$.